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Contingent epiderivatives and set-valued optimization

Contingent epiderivatives and set-valued optimization In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Methods of Operations Research Springer Journals

Contingent epiderivatives and set-valued optimization

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References (9)

Publisher
Springer Journals
Copyright
Copyright © 1997 by Physica-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Operation Research/Decision Theory; Business and Management, general
ISSN
1432-2994
eISSN
1432-5217
DOI
10.1007/BF01217690
Publisher site
See Article on Publisher Site

Abstract

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.

Journal

Mathematical Methods of Operations ResearchSpringer Journals

Published: Feb 5, 2005

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